A) Erdos Renyi Graph

B) Complemente

C) Adjecency Materix

Matrix

30 x 30 sparse Matrix of class "dgCMatrix"
                                                                 
 [1,] . . . . 1 . . . . 1 . 1 . . . . . . . . . . . . . . 1 . 1 1
 [2,] . . 1 1 . . . . . . . 1 . . . . . . . . 1 . 1 . . 1 . 1 . .
 [3,] . 1 . . . . . . . . . . . 1 . . 1 . . 1 . . . . . 1 . . . .
 [4,] . 1 . . . . . 1 . . . . . . . . . . . . . . . . . . . . . .
 [5,] 1 . . . . . . . . . 1 . . . . . . 1 . . 1 . . . . . 1 1 . .
 [6,] . . . . . . 1 1 . . . . . . 1 . 1 . . 1 . . . . . . . . . .
 [7,] . . . . . 1 . . 1 1 . . . . . . . . . . . . . . . . 1 . . 1
 [8,] . . . 1 . 1 . . 1 . . . 1 . 1 . . . . . . 1 1 . . . . 1 . .
 [9,] . . . . . . 1 1 . 1 . 1 1 . 1 . . . 1 . . . . . . . . . . .
[10,] 1 . . . . . 1 . 1 . . 1 1 . 1 . 1 1 . . . . . . . . 1 . 1 .
[11,] . . . . 1 . . . . . . . 1 . . 1 1 . 1 . . 1 . . . . . . . .
[12,] 1 1 . . . . . . 1 1 . . . . . . . 1 . 1 . 1 . 1 1 . . . . .
[13,] . . . . . . . 1 1 1 1 . . 1 . . . . . . . . . . . . . . . .
[14,] . . 1 . . . . . . . . . 1 . . . 1 . . . . . . . . . 1 . 1 .
[15,] . . . . . 1 . 1 1 1 . . . . . . . . . . . . . . . . . . . 1
[16,] . . . . . . . . . . 1 . . . . . 1 . . 1 . . . . 1 . . 1 . .
[17,] . . 1 . . 1 . . . 1 1 . . 1 . 1 . . 1 . . . . . . . . . . .
[18,] . . . . 1 . . . . 1 . 1 . . . . . . 1 . . 1 . 1 . . . . . .
[19,] . . . . . . . . 1 . 1 . . . . . 1 1 . . . 1 . 1 . . . . . .
[20,] . . 1 . . 1 . . . . . 1 . . . 1 . . . . 1 . . . . 1 1 1 . .
[21,] . 1 . . 1 . . . . . . . . . . . . . . 1 . . . 1 . . . . . 1
[22,] . . . . . . . 1 . . 1 1 . . . . . 1 1 . . . . 1 1 . . . . .
[23,] . 1 . . . . . 1 . . . . . . . . . . . . . . . . . . . . . .
[24,] . . . . . . . . . . . 1 . . . . . 1 1 . 1 1 . . . 1 . 1 1 .
[25,] . . . . . . . . . . . 1 . . . 1 . . . . . 1 . . . . . . 1 1
[26,] . 1 1 . . . . . . . . . . . . . . . . 1 . . . 1 . . . . 1 .
[27,] 1 . . . 1 . 1 . . 1 . . . 1 . . . . . 1 . . . . . . . . . .
[28,] . 1 . . 1 . . 1 . . . . . . . 1 . . . 1 . . . 1 . . . . . 1
[29,] 1 . . . . . . . . 1 . . . 1 . . . . . . . . . 1 1 1 . . . 1
[30,] 1 . . . . . 1 . . . . . . . 1 . . . . . 1 . . . 1 . . 1 1 .

D) Some powers of the matrix

Matrix^2

30 x 30 sparse Matrix of class "dgCMatrix"
                                                                  
 [1,] 6 1 . . 1 . 3 . 2  3 1 1 1 2 2 . 1 3 . 2 2 1 . 2 3 1 2 2 2 1
 [2,] 1 7 1 . 2 . . 3 1  1 . . . 1 . 1 1 1 . 5 . 1 . 4 1 1 . . 1 2
 [3,] . 1 5 1 . 2 . . .  1 1 2 1 1 . 2 1 . 1 1 2 . 1 1 . 2 2 2 2 .
 [4,] . . 1 2 . 1 . . 1  . . 1 1 . 1 . . . . . 1 1 2 . . 1 . 2 . .
 [5,] 1 2 . . 6 . 1 1 .  3 . 2 1 1 . 2 1 . 2 3 . 2 . 3 . . 1 . 1 3
 [6,] . . 2 1 . 5 . 1 3  3 1 1 1 1 1 2 . . 1 . 1 1 1 . . 1 2 2 . 2
 [7,] 3 . . . 1 . 5 2 1  2 . 2 2 1 4 . 2 1 1 2 1 . . . 1 . 1 1 2 .
 [8,] . 3 . . 1 1 2 8 2  3 2 2 1 1 2 1 1 1 2 2 . . . 2 1 . . . . 2
 [9,] 2 1 . 1 . 3 1 2 7  4 2 1 2 1 2 . 2 3 . 1 . 3 1 2 1 . 2 1 1 2
[10,] 3 1 1 . 3 3 2 3 4 10 2 3 1 4 1 1 . 1 3 2 . 2 . 3 2 1 2 . 1 4
[11,] 1 . 1 . . 1 . 2 2  2 6 1 . 2 . 1 2 3 2 1 1 1 . 2 2 . 1 2 . .
[12,] 1 . 2 1 2 1 2 2 1  3 1 9 2 . 2 2 1 3 4 . 3 3 1 2 1 3 3 3 4 2
[13,] 1 . 1 1 1 1 2 1 2  1 . 2 5 . 3 1 3 1 2 . . 2 1 . . . 2 1 2 .
[14,] 2 1 1 . 1 1 1 1 1  4 2 . . 5 . 1 1 . 1 2 . . . 1 1 2 . . . 1
[15,] 2 . . 1 . 1 4 2 2  1 . 2 3 . 5 . 2 1 1 1 1 1 1 . 1 . 1 2 2 .
[16,] . 1 2 . 2 2 . 1 .  1 1 2 1 1 . 5 1 . 2 1 1 2 . 1 . 1 1 1 1 2
[17,] 1 1 1 . 1 . 2 1 2  . 2 1 3 1 2 1 7 2 1 3 . 2 . 1 1 1 2 1 2 .
[18,] 3 1 . . . . 1 1 3  1 3 3 1 . 1 . 2 6 2 1 2 3 . 3 2 1 2 2 2 .
[19,] . . 1 . 2 1 1 2 .  3 2 4 2 1 1 2 1 2 6 . 1 3 . 2 1 1 . 1 1 .
[20,] 2 5 1 . 3 . 2 2 1  2 1 . . 2 1 1 3 1 . 8 . 1 . 4 2 1 . 1 1 2
[21,] 2 . 2 1 . 1 1 . .  . 1 3 . . 1 1 . 2 1 . 5 1 1 . 1 3 2 5 2 .
[22,] 1 1 . 1 2 1 . . 3  2 1 3 2 . 1 2 2 3 3 1 1 7 1 3 1 1 . 2 2 1
[23,] . . 1 2 . 1 . . 1  . . 1 1 . 1 . . . . . 1 1 2 . . 1 . 2 . .
[24,] 2 4 1 . 3 . . 2 2  3 2 2 . 1 . 1 1 3 2 4 . 3 . 8 3 1 . . 1 3
[25,] 3 1 . . . . 1 1 1  2 2 1 . 1 1 . 1 2 1 2 1 1 . 3 5 1 . 2 1 1
[26,] 1 1 2 1 . 1 . . .  1 . 3 . 2 . 1 1 1 1 1 3 1 1 1 1 5 1 3 1 1
[27,] 2 . 2 . 1 2 1 . 2  2 1 3 2 . 1 1 2 2 . . 2 . . . . 1 6 2 3 2
[28,] 2 . 2 2 . 2 1 . 1  . 2 3 1 . 2 1 1 2 1 1 5 2 2 . 2 3 2 7 2 .
[29,] 2 1 2 . 1 . 2 . 1  1 . 4 2 . 2 1 2 2 1 1 2 2 . 1 1 1 3 2 7 2
[30,] 1 2 . . 3 2 . 2 2  4 . 2 . 1 . 2 . . . 2 . 1 . 3 1 1 2 . 2 7

Matrix^5

30 x 30 sparse Matrix of class "dgCMatrix"
                                                                       
 [1,] 474 345 312 104 482 350 368 419 505  808 321  789 366 305 348 370
 [2,] 345 156 377 198 199 310 256 201 314  395 273  709 297 168 312 288
 [3,] 312 377 194  55 292 155 224 299 291  429 237  331 177 260 192 209
 [4,] 104 198  55  12 135  64  91 205 133  202  97  129  64  97  80  85
 [5,] 482 199 292 135 218 275 321 257 433  491 382  639 302 215 341 240
 [6,] 350 310 155  64 275 164 356 385 358  450 244  400 289 216 342 184
 [7,] 368 256 224  91 321 356 258 354 504  701 289  511 272 277 264 264
 [8,] 419 201 299 205 257 385 354 326 560  568 329  676 437 204 444 286
 [9,] 505 314 291 133 433 358 504 560 570  833 389  838 481 322 508 348
[10,] 808 395 429 202 491 450 701 568 833  948 534 1124 698 360 733 417
[11,] 321 273 237  97 382 244 289 329 389  534 290  597 363 215 304 327
[12,] 789 709 331 129 639 400 511 676 838 1124 597  862 436 507 481 418
[13,] 366 297 177  64 302 289 272 437 481  698 363  436 234 328 254 228
[14,] 305 168 260  97 215 216 277 204 322  360 215  507 328 144 299 226
[15,] 348 312 192  80 341 342 264 444 508  733 304  481 254 299 264 262
[16,] 370 288 209  85 240 184 264 286 348  417 327  418 228 226 262 204
[17,] 378 289 326 107 370 386 275 414 468  767 409  624 295 368 266 368
[18,] 469 409 287 109 535 329 348 483 532  859 401  809 366 338 334 396
[19,] 466 366 228 103 352 271 311 403 574  643 445  603 343 274 332 279
[20,] 454 232 485 212 318 442 336 309 453  617 377  905 395 258 385 422
[21,] 342 514 170  33 456 172 217 398 350  589 241  389 163 278 168 266
[22,] 516 417 289 108 432 303 378 545 557  789 508  801 355 330 374 350
[23,] 104 198  55  12 135  64  91 205 133  202  97  129  64  97  80  85
[24,] 581 300 447 215 400 388 433 385 553  705 465 1072 479 267 482 427
[25,] 336 262 263 104 358 267 260 299 376  546 253  660 305 193 275 323
[26,] 344 438 235  62 353 172 234 329 323  478 247  435 201 236 209 250
[27,] 503 410 206  59 444 249 387 431 459  768 321  509 274 382 319 267
[28,] 423 634 243  54 575 263 301 568 468  782 340  555 246 363 250 377
[29,] 569 465 271  87 473 327 354 471 550  896 411  641 265 432 303 325
[30,] 568 240 297 152 267 266 460 313 451  542 333  713 383 232 473 245
                                                              
 [1,] 378 469 466 454 342 516 104  581 336 344 503 423 569 568
 [2,] 289 409 366 232 514 417 198  300 262 438 410 634 465 240
 [3,] 326 287 228 485 170 289  55  447 263 235 206 243 271 297
 [4,] 107 109 103 212  33 108  12  215 104  62  59  54  87 152
 [5,] 370 535 352 318 456 432 135  400 358 353 444 575 473 267
 [6,] 386 329 271 442 172 303  64  388 267 172 249 263 327 266
 [7,] 275 348 311 336 217 378  91  433 260 234 387 301 354 460
 [8,] 414 483 403 309 398 545 205  385 299 329 431 568 471 313
 [9,] 468 532 574 453 350 557 133  553 376 323 459 468 550 451
[10,] 767 859 643 617 589 789 202  705 546 478 768 782 896 542
[11,] 409 401 445 377 241 508  97  465 253 247 321 340 411 333
[12,] 624 809 603 905 389 801 129 1072 660 435 509 555 641 713
[13,] 295 366 343 395 163 355  64  479 305 201 274 246 265 383
[14,] 368 338 274 258 278 330  97  267 193 236 382 363 432 232
[15,] 266 334 332 385 168 374  80  482 275 209 319 250 303 473
[16,] 368 396 279 422 266 350  85  427 323 250 267 377 325 245
[17,] 332 401 474 397 295 453 107  511 316 326 372 392 370 429
[18,] 401 542 589 521 314 644 109  728 397 347 395 411 504 540
[19,] 474 589 434 488 280 580 103  636 399 275 362 410 433 377
[20,] 397 521 488 332 603 534 212  426 330 524 580 739 611 402
[21,] 295 314 280 603 118 370  33  649 307 208 211 176 301 484
[22,] 453 644 580 534 370 610 108  737 475 358 399 486 502 458
[23,] 107 109 103 212  33 108  12  215 104  62  59  54  87 152
[24,] 511 728 636 426 649 737 215  610 455 550 588 804 733 420
[25,] 316 397 399 330 307 475 104  455 258 296 373 385 470 405
[26,] 326 347 275 524 208 358  62  550 296 250 258 278 365 372
[27,] 372 395 362 580 211 399  59  588 373 258 322 293 385 463
[28,] 392 411 410 739 176 486  54  804 385 278 293 256 396 618
[29,] 370 504 433 611 301 502  87  733 470 365 385 396 446 575
[30,] 429 540 377 402 484 458 152  420 405 372 463 618 575 300

Matrix^15

30 x 30 sparse Matrix of class "dgCMatrix"
                                                                  
 [1,]  72118205790 54352544364 43836728641 17994462569 59474601910
 [2,]  54352544364 40335196498 33325978240 13801650295 44382822339
 [3,]  43836728641 33325978240 26518368688 10835263403 36295657186
 [4,]  17994462569 13801650295 10835263403  4404717698 14985128733
 [5,]  59474601910 44382822339 36295657186 14985128733 48697978194
 [6,]  47325236414 35781883233 28662310425 11748214669 39054602321
 [7,]  54818954800 41390322666 33272478497 13643971580 45256718151
 [8,]  63492844622 47396822766 38744195915 15995919140 52027719896
 [9,]  76876702780 57808620468 46732246540 19210418936 63295362464
[10,] 105854153738 79240481609 64458522786 26566208823 86863649104
[11,]  56471939980 42528649324 34332945580 14103718074 46541268403
[12,] 104058647790 78914929176 62980493224 25768751012 86053906999
[13,]  53155663820 40319418807 32164467852 13156344471 43986588720
[14,]  45382237059 33880586086 27698591447 11432590814 37187988283
[15,]  54928574024 41653437690 33261754807 13606707920 45465922079
[16,]  48709593706 36708677112 29574775170 12145339205 40108089295
[17,]  63289085095 47750943044 38457828716 15777651658 52228088577
[18,]  76625299858 57928430612 46502969529 19058842340 63305628840
[19,]  67047138557 50599025289 40673450072 16690089355 55282889541
[20,]  73086885987 54438045746 44728224058 18484199057 59829486467
[21,]  51993913586 39826504134 31347725794 12751385141 43272710208
[22,]  78164888644 58987646917 47447979639 19467765737 64469815916
[23,]  17994462569 13801650295 10835263403  4404717698 14985128733
[24,]  87353354673 65194527888 53359617687 22029673130 71574060151
[25,]  56671183396 42593271421 34510283951 14190510817 46657337180
[26,]  50806211397 38594154713 30760312215 12574082331 42057524375
[27,]  62739989064 47645235305 37944041137 15509032130 51939685759
[28,]  69116273892 52824871581 41721499360 16993101981 57456179086
[29,]  73991533968 56121974736 44803921234 18326010245 61216423388
[30,]  66300094770 49495257279 40434328335 16690258043 54293978726
                                                                   
 [1,] 47325236414 54818954800 63492844622  76876702780 105854153738
 [2,] 35781883233 41390322666 47396822766  57808620468  79240481609
 [3,] 28662310425 33272478497 38744195915  46732246540  64458522786
 [4,] 11748214669 13643971580 15995919140  19210418936  26566208823
 [5,] 39054602321 45256718151 52027719896  63295362464  86863649104
 [6,] 30963510296 35974017453 41726566122  50442059957  69456136431
 [7,] 35974017453 41654730940 48333809935  58475979546  80561770884
 [8,] 41726566122 48333809935 55595166344  67619371833  92811711252
 [9,] 50442059957 58475979546 67619371833  81941888228 112728868826
[10,] 69456136431 80561770884 92811711252 112728868826 154828511500
[11,] 37044169298 42939770370 49693669835  60190845448  82828135482
[12,] 68091085779 79006220777 91888802528 110957673654 152959060658
[13,] 34820917083 40363461064 46989436980  56723280168  78230006845
[14,] 29809334648 34553850704 39723715821  48311355248  66308014298
[15,] 36009939971 41714307269 48557581921  58624211843  80861969636
[16,] 31897778776 37016533459 42840504475  51882862147  71377079285
[17,] 41545552586 48088996257 55770481299  67491705620  92969628721
[18,] 50240070230 58212119444 67579186178  81708931865 112592052044
[19,] 43918520921 50945530010 59049044586  71466551260  98369402827
[20,] 48093953217 55632984337 63887124126  77785914918 106747668090
[21,] 33961808110 39417821464 46164405124  55487742842  76719113985
[22,] 51227127029 59392441223 68849856951  83315105282 114713649640
[23,] 11748214669 13643971580 15995919140  19210418936  26566208823
[24,] 57401899292 66478707311 76435500254  92977526146 127628888099
[25,] 37209723508 43092473403 49804852821  60384943563  83071465586
[26,] 33233758309 38565295259 44882641417  54157766899  74691137459
[27,] 41052471167 47636893559 55461326271  66915001359  92303867304
[28,] 45184179951 52421718737 61307296022  73758170196 101925604334
[29,] 48451397943 56169319779 65355811791  78907058539 108823969049
[30,] 43510650887 50465253616 58010892974  70552012509  96823599374
                                                                  
 [1,] 56471939980 104058647790 53155663820 45382237059 54928574024
 [2,] 42528649324  78914929176 40319418807 33880586086 41653437690
 [3,] 34332945580  62980493224 32164467852 27698591447 33261754807
 [4,] 14103718074  25768751012 13156344471 11432590814 13606707920
 [5,] 46541268403  86053906999 43986588720 37187988283 45465922079
 [6,] 37044169298  68091085779 34820917083 29809334648 36009939971
 [7,] 42939770370  79006220777 40363461064 34553850704 41714307269
 [8,] 49693669835  91888802528 46989436980 39723715821 48557581921
 [9,] 60190845448 110957673654 56723280168 48311355248 58624211843
[10,] 82828135482 152959060658 78230006845 66308014298 80861969636
[11,] 44224214332  81507795954 41653140775 35504095317 43040417595
[12,] 81507795954 149623357088 76430883381 65682941238 79027225717
[13,] 41653140775  76430883381 39047153264 33591026068 40368174463
[14,] 35504095317  65682941238 33591026068 28380547854 34712028279
[15,] 43040417595  79027225717 40368174463 34712028279 41724840098
[16,] 38134808288  70192944294 35870824171 30620630147 37090836665
[17,] 49588551160  91285021955 46618276387 39873229580 48172693533
[18,] 60029840937 110438526907 56400517776 48300117823 58284155161
[19,] 52511936930  96592951927 49363213586 42197715818 51030102249
[20,] 57202089756 105970818334 54138917562 45669824820 55929500872
[21,] 40745531396  74522651700 38031739755 33005231969 39325347818
[22,] 61226983571 112666979129 57554904286 49205161822 59491748764
[23,] 14103718074  25768751012 13156344471 11432590814 13606707920
[24,] 68370237529 126506899364 64644532029 54623908969 66794805606
[25,] 44373965658  81886148952 41829032739 35593374298 43216931645
[26,] 39790773078  73048840368 37298863444 32084439287 38563943627
[27,] 49137872246  90159220901 46058409145 39647596899 47625440367
[28,] 54164051352  99165921119 50616516879 43827164563 52331377546
[29,] 57963241957 106418960962 54339421890 46731611807 56179204908
[30,] 51862657690  95888712622 49032568198 41454848063 50689269617
                                                                   
 [1,] 48709593706 63289085095  76625299858 67047138557  73086885987
 [2,] 36708677112 47750943044  57928430612 50599025289  54438045746
 [3,] 29574775170 38457828716  46502969529 40673450072  44728224058
 [4,] 12145339205 15777651658  19058842340 16690089355  18484199057
 [5,] 40108089295 52228088577  63305628840 55282889541  59829486467
 [6,] 31897778776 41545552586  50240070230 43918520921  48093953217
 [7,] 37016533459 48088996257  58212119444 50945530010  55632984337
 [8,] 42840504475 55770481299  67579186178 59049044586  63887124126
 [9,] 51882862147 67491705620  81708931865 71466551260  77785914918
[10,] 71377079285 92969628721 112592052044 98369402827 106747668090
[11,] 38134808288 49588551160  60029840937 52511936930  57202089756
[12,] 70192944294 91285021955 110438526907 96592951927 105970818334
[13,] 35870824171 46618276387  56400517776 49363213586  54138917562
[14,] 30620630147 39873229580  48300117823 42197715818  45669824820
[15,] 37090836665 48172693533  58284155161 51030102249  55929500872
[16,] 32840955628 42757530269  51756818534 45222857396  49372173692
[17,] 42757530269 55528216560  67237199336 58849691274  64191373146
[18,] 51756818534 67237199336  81391367694 71234530122  77836711654
[19,] 45222857396 58849691274  71234530122 62275757404  68026510273
[20,] 49372173692 64191373146  77836711654 68026510273  73405920332
[21,] 35107784362 45584550664  55087378439 48238356659  53350863880
[22,] 52752615499 68598502160  83051663261 72636263776  79299486052
[23,] 12145339205 15777651658  19058842340 16690089355  18484199057
[24,] 58970546573 76725466532  93007930256 81269667874  87873468569
[25,] 38285339766 49753369420  60260767921 52713806985  57310413125
[26,] 34291770445 44575201838  53913261169 47160645037  51804361969
[27,] 42325526388 55027383474  66548800483 58229026235  63962236813
[28,] 46677828435 60607374404  73259612494 64153235848  70799567139
[29,] 49939032580 64887224392  78516243304 68702487592  75355178619
[30,] 44692696508 58229680976  70551533734 61604512908  66721206167
                                                                   
 [1,] 51993913586  78164888644 17994462569  87353354673 56671183396
 [2,] 39826504134  58987646917 13801650295  65194527888 42593271421
 [3,] 31347725794  47447979639 10835263403  53359617687 34510283951
 [4,] 12751385141  19467765737  4404717698  22029673130 14190510817
 [5,] 43272710208  64469815916 14985128733  71574060151 46657337180
 [6,] 33961808110  51227127029 11748214669  57401899292 37209723508
 [7,] 39417821464  59392441223 13643971580  66478707311 43092473403
 [8,] 46164405124  68849856951 15995919140  76435500254 49804852821
 [9,] 55487742842  83315105282 19210418936  92977526146 60384943563
[10,] 76719113985 114713649640 26566208823 127628888099 83071465586
[11,] 40745531396  61226983571 14103718074  68370237529 44373965658
[12,] 74522651700 112666979129 25768751012 126506899364 81886148952
[13,] 38031739755  57554904286 13156344471  64644532029 41829032739
[14,] 33005231969  49205161822 11432590814  54623908969 35593374298
[15,] 39325347818  59491748764 13606707920  66794805606 43216931645
[16,] 35107784362  52752615499 12145339205  58970546573 38285339766
[17,] 45584550664  68598502160 15777651658  76725466532 49753369420
[18,] 55087378439  83051663261 19058842340  93007930256 60260767921
[19,] 48238356659  72636263776 16690089355  81269667874 52713806985
[20,] 53350863880  79299486052 18484199057  87873468569 57310413125
[21,] 36917156960  56269761054 12751385141  63607641490 40992347085
[22,] 56269761054  84699559538 19467765737  94755882016 61456601370
[23,] 12751385141  19467765737  4404717698  22029673130 14190510817
[24,] 63607641490  94755882016 22029673130 105157185886 68529425667
[25,] 40992347085  61456601370 14190510817  68529425667 44512882046
[26,] 36376654859  55013159007 12574082331  61820979109 39991069338
[27,] 44855455341  67907268307 15509032130  76332861157 49376336004
[28,] 49178890155  74822246173 16993101981  84443053248 54467614260
[29,] 52997684667  80117214892 18326010245  89971906922 58226170963
[30,] 48199865803  71845480992 16690258043  79789291999 52007300193
                                                                   
 [1,] 50806211397 62739989064  69116273892  73991533968 66300094770
 [2,] 38594154713 47645235305  52824871581  56121974736 49495257279
 [3,] 30760312215 37944041137  41721499360  44803921234 40434328335
 [4,] 12574082331 15509032130  16993101981  18326010245 16690258043
 [5,] 42057524375 51939685759  57456179086  61216423388 54293978726
 [6,] 33233758309 41052471167  45184179951  48451397943 43510650887
 [7,] 38565295259 47636893559  52421718737  56169319779 50465253616
 [8,] 44882641417 55461326271  61307296022  65355811791 58010892974
 [9,] 54157766899 66915001359  73758170196  78907058539 70552012509
[10,] 74691137459 92303867304 101925604334 108823969049 96823599374
[11,] 39790773078 49137872246  54164051352  57963241957 51862657690
[12,] 73048840368 90159220901  99165921119 106418960962 95888712622
[13,] 37298863444 46058409145  50616516879  54339421890 49032568198
[14,] 32084439287 39647596899  43827164563  46731611807 41454848063
[15,] 38563943627 47625440367  52331377546  56179204908 50689269617
[16,] 34291770445 42325526388  46677828435  49939032580 44692696508
[17,] 44575201838 55027383474  60607374404  64887224392 58229680976
[18,] 53913261169 66548800483  73259612494  78516243304 70551533734
[19,] 47160645037 58229026235  64153235848  68702487592 61604512908
[20,] 51804361969 63962236813  70799567139  75355178619 66721206167
[21,] 36376654859 44855455341  49178890155  52997684667 48199865803
[22,] 55013159007 67907268307  74822246173  80117214892 71845480992
[23,] 12574082331 15509032130  16993101981  18326010245 16690258043
[24,] 61820979109 76332861157  84443053248  89971906922 79789291999
[25,] 39991069338 49376336004  54467614260  58226170963 52007300193
[26,] 35677952100 44007750124  48403798904  51962395508 46853399799
[27,] 44007750124 54328033928  59700271047  64124595334 57879636058
[28,] 48403798904 59700271047  65495036128  70515840499 64006103947
[29,] 51962395508 64124595334  70515840499  75672206978 68229285112
[30,] 46853399799 57879636058  64006103947  68229285112 60523427564

Matrix^30

30 x 30 sparse Matrix of class "dgCMatrix"
                                                                      
 [1,] 1.254795e+23 9.454107e+22 7.623880e+22 3.130733e+22 1.033983e+23
 [2,] 9.454107e+22 7.123507e+22 5.743951e+22 2.358664e+22 7.790705e+22
 [3,] 7.623880e+22 5.743951e+22 4.632189e+22 1.902232e+22 6.282160e+22
 [4,] 3.130733e+22 2.358664e+22 1.902232e+22 7.811764e+21 2.579705e+22
 [5,] 1.033983e+23 7.790705e+22 6.282160e+22 2.579705e+22 8.520474e+22
 [6,] 8.227799e+22 6.199057e+22 4.999079e+22 2.052878e+22 6.779865e+22
 [7,] 9.537673e+22 7.185985e+22 5.794922e+22 2.379686e+22 7.859245e+22
 [8,] 1.104200e+23 8.319749e+22 6.708781e+22 2.754896e+22 9.099080e+22
 [9,] 1.337235e+23 1.007531e+23 8.124742e+22 3.336398e+22 1.101920e+23
[10,] 1.840435e+23 1.386686e+23 1.118198e+23 4.591798e+22 1.516587e+23
[11,] 9.825466e+22 7.402909e+22 5.969744e+22 2.451460e+22 8.096454e+22
[12,] 1.809724e+23 1.363484e+23 1.099565e+23 4.515405e+22 1.491238e+23
[13,] 9.246734e+22 6.966660e+22 5.618204e+22 2.307140e+22 7.619425e+22
[14,] 7.891898e+22 5.946265e+22 4.794872e+22 1.968967e+22 6.503264e+22
[15,] 9.557574e+22 7.200864e+22 5.807062e+22 2.384693e+22 7.875568e+22
[16,] 8.468550e+22 6.380534e+22 5.145320e+22 2.112916e+22 6.978306e+22
[17,] 1.101338e+23 8.297866e+22 6.691521e+22 2.747868e+22 9.075284e+22
[18,] 1.333355e+23 1.004590e+23 8.101243e+22 3.326782e+22 1.098712e+23
[19,] 1.165995e+23 8.785007e+22 7.084374e+22 2.909195e+22 9.608070e+22
[20,] 1.271475e+23 9.580209e+22 7.725046e+22 3.172196e+22 1.047756e+23
[21,] 9.046767e+22 6.815789e+22 5.496796e+22 2.257323e+22 7.454509e+22
[22,] 1.359648e+23 1.024406e+23 8.260969e+22 3.392362e+22 1.120382e+23
[23,] 3.130733e+22 2.358664e+22 1.902232e+22 7.811764e+21 2.579705e+22
[24,] 1.519363e+23 1.144789e+23 9.231171e+22 3.790684e+22 1.252023e+23
[25,] 9.860985e+22 7.429730e+22 5.991299e+22 2.460300e+22 8.125761e+22
[26,] 8.837514e+22 6.658347e+22 5.369569e+22 2.205037e+22 7.282224e+22
[27,] 1.091174e+23 8.221083e+22 6.629853e+22 2.722583e+22 8.991396e+22
[28,] 1.202696e+23 9.061119e+22 7.307522e+22 3.000906e+22 9.910223e+22
[29,] 1.287064e+23 9.697001e+22 7.820038e+22 3.211328e+22 1.060558e+23
[30,] 1.152456e+23 8.683338e+22 7.001968e+22 2.875290e+22 9.496729e+22
                                                                      
 [1,] 8.227799e+22 9.537673e+22 1.104200e+23 1.337235e+23 1.840435e+23
 [2,] 6.199057e+22 7.185985e+22 8.319749e+22 1.007531e+23 1.386686e+23
 [3,] 4.999079e+22 5.794922e+22 6.708781e+22 8.124742e+22 1.118198e+23
 [4,] 2.052878e+22 2.379686e+22 2.754896e+22 3.336398e+22 4.591798e+22
 [5,] 6.779865e+22 7.859245e+22 9.099080e+22 1.101920e+23 1.516587e+23
 [6,] 5.395057e+22 6.253946e+22 7.240282e+22 8.768353e+22 1.206783e+23
 [7,] 6.253946e+22 7.249577e+22 8.392963e+22 1.016429e+23 1.398906e+23
 [8,] 7.240282e+22 8.392963e+22 9.716981e+22 1.176751e+23 1.619576e+23
 [9,] 8.768353e+22 1.016429e+23 1.176751e+23 1.425092e+23 1.961356e+23
[10,] 1.206783e+23 1.398906e+23 1.619576e+23 1.961356e+23 2.699430e+23
[11,] 6.442638e+22 7.468314e+22 8.646276e+22 1.047100e+23 1.441124e+23
[12,] 1.186658e+23 1.375573e+23 1.592508e+23 1.928618e+23 2.654337e+23
[13,] 6.063199e+22 7.028452e+22 8.136860e+22 9.854215e+22 1.356224e+23
[14,] 5.174746e+22 5.998585e+22 6.944887e+22 8.410428e+22 1.157537e+23
[15,] 6.267018e+22 7.264721e+22 8.410398e+22 1.018548e+23 1.401816e+23
[16,] 5.552902e+22 6.436927e+22 7.452196e+22 9.024934e+22 1.242101e+23
[17,] 7.221574e+22 8.371255e+22 9.691580e+22 1.173695e+23 1.615353e+23
[18,] 8.742947e+22 1.013483e+23 1.173325e+23 1.420955e+23 1.955652e+23
[19,] 7.645544e+22 8.862716e+22 1.026055e+23 1.242601e+23 1.710187e+23
[20,] 8.337086e+22 9.664391e+22 1.118907e+23 1.355017e+23 1.864932e+23
[21,] 5.932120e+22 6.876488e+22 7.960752e+22 9.641077e+22 1.326879e+23
[22,] 8.915341e+22 1.033467e+23 1.196466e+23 1.448976e+23 1.994221e+23
[23,] 2.052878e+22 2.379686e+22 2.754896e+22 3.336398e+22 4.591798e+22
[24,] 9.962515e+22 1.154859e+23 1.337045e+23 1.619192e+23 2.228515e+23
[25,] 6.465915e+22 7.495302e+22 8.677571e+22 1.050886e+23 1.446338e+23
[26,] 5.794870e+22 6.717403e+22 7.776758e+22 9.418111e+22 1.296204e+23
[27,] 7.154971e+22 8.294029e+22 9.602003e+22 1.162860e+23 1.600430e+23
[28,] 7.886266e+22 9.141733e+22 1.058323e+23 1.281705e+23 1.763985e+23
[29,] 8.439436e+22 9.782984e+22 1.132581e+23 1.371620e+23 1.887746e+23
[30,] 7.556697e+22 8.759750e+22 1.014163e+23 1.228177e+23 1.690354e+23
                                                                      
 [1,] 9.825466e+22 1.809724e+23 9.246734e+22 7.891898e+22 9.557574e+22
 [2,] 7.402909e+22 1.363484e+23 6.966660e+22 5.946265e+22 7.200864e+22
 [3,] 5.969744e+22 1.099565e+23 5.618204e+22 4.794872e+22 5.807062e+22
 [4,] 2.451460e+22 4.515405e+22 2.307140e+22 1.968967e+22 2.384693e+22
 [5,] 8.096454e+22 1.491238e+23 7.619425e+22 6.503264e+22 7.875568e+22
 [6,] 6.442638e+22 1.186658e+23 6.063199e+22 5.174746e+22 6.267018e+22
 [7,] 7.468314e+22 1.375573e+23 7.028452e+22 5.998585e+22 7.264721e+22
 [8,] 8.646276e+22 1.592508e+23 8.136860e+22 6.944887e+22 8.410398e+22
 [9,] 1.047100e+23 1.928618e+23 9.854215e+22 8.410428e+22 1.018548e+23
[10,] 1.441124e+23 2.654337e+23 1.356224e+23 1.157537e+23 1.401816e+23
[11,] 7.693672e+22 1.417073e+23 7.240491e+22 6.179634e+22 7.483890e+22
[12,] 1.417073e+23 2.610094e+23 1.333621e+23 1.138191e+23 1.378452e+23
[13,] 7.240491e+22 1.333621e+23 6.814109e+22 5.815543e+22 7.043169e+22
[14,] 6.179634e+22 1.138191e+23 5.815543e+22 4.963626e+22 6.011044e+22
[15,] 7.483890e+22 1.378452e+23 7.043169e+22 6.011044e+22 7.279929e+22
[16,] 6.631160e+22 1.221374e+23 6.240574e+22 5.326205e+22 6.450358e+22
[17,] 8.623844e+22 1.588404e+23 8.115907e+22 6.926728e+22 8.388732e+22
[18,] 1.044061e+23 1.923036e+23 9.825703e+22 8.385940e+22 1.015600e+23
[19,] 9.130133e+22 1.681657e+23 8.592381e+22 7.333378e+22 8.881223e+22
[20,] 9.956102e+22 1.833748e+23 9.369461e+22 7.997015e+22 9.684438e+22
[21,] 7.083898e+22 1.304797e+23 6.666842e+22 5.689673e+22 6.890945e+22
[22,] 1.064650e+23 1.960952e+23 1.001943e+23 8.551336e+22 1.035625e+23
[23,] 2.451460e+22 4.515405e+22 2.307140e+22 1.968967e+22 2.384693e+22
[24,] 1.189715e+23 2.191265e+23 1.119618e+23 9.556080e+22 1.157257e+23
[25,] 7.721487e+22 1.422191e+23 7.266639e+22 6.202001e+22 7.510918e+22
[26,] 6.920060e+22 1.274601e+23 6.512546e+22 5.558173e+22 6.731469e+22
[27,] 8.544245e+22 1.573761e+23 8.041097e+22 6.862703e+22 8.311402e+22
[28,] 9.417482e+22 1.734618e+23 8.863004e+22 7.564002e+22 9.160932e+22
[29,] 1.007813e+23 1.856282e+23 9.484630e+22 8.094735e+22 9.803461e+22
[30,] 9.024135e+22 1.662104e+23 8.492455e+22 7.248392e+22 8.777947e+22
                                                                      
 [1,] 8.468550e+22 1.101338e+23 1.333355e+23 1.165995e+23 1.271475e+23
 [2,] 6.380534e+22 8.297866e+22 1.004590e+23 8.785007e+22 9.580209e+22
 [3,] 5.145320e+22 6.691521e+22 8.101243e+22 7.084374e+22 7.725046e+22
 [4,] 2.112916e+22 2.747868e+22 3.326782e+22 2.909195e+22 3.172196e+22
 [5,] 6.978306e+22 9.075284e+22 1.098712e+23 9.608070e+22 1.047756e+23
 [6,] 5.552902e+22 7.221574e+22 8.742947e+22 7.645544e+22 8.337086e+22
 [7,] 6.436927e+22 8.371255e+22 1.013483e+23 8.862716e+22 9.664391e+22
 [8,] 7.452196e+22 9.691580e+22 1.173325e+23 1.026055e+23 1.118907e+23
 [9,] 9.024934e+22 1.173695e+23 1.420955e+23 1.242601e+23 1.355017e+23
[10,] 1.242101e+23 1.615353e+23 1.955652e+23 1.710187e+23 1.864932e+23
[11,] 6.631160e+22 8.623844e+22 1.044061e+23 9.130133e+22 9.956102e+22
[12,] 1.221374e+23 1.588404e+23 1.923036e+23 1.681657e+23 1.833748e+23
[13,] 6.240574e+22 8.115907e+22 9.825703e+22 8.592381e+22 9.369461e+22
[14,] 5.326205e+22 6.926728e+22 8.385940e+22 7.333378e+22 7.997015e+22
[15,] 6.450358e+22 8.388732e+22 1.015600e+23 8.881223e+22 9.684438e+22
[16,] 5.715385e+22 7.432875e+22 8.998749e+22 7.869247e+22 8.581124e+22
[17,] 7.432875e+22 9.666486e+22 1.170292e+23 1.023399e+23 1.115974e+23
[18,] 8.998749e+22 1.170292e+23 1.416837e+23 1.238998e+23 1.351068e+23
[19,] 7.869247e+22 1.023399e+23 1.238998e+23 1.083481e+23 1.181490e+23
[20,] 8.581124e+22 1.115974e+23 1.351068e+23 1.181490e+23 1.288420e+23
[21,] 6.105617e+22 7.940413e+22 9.613271e+22 8.406591e+22 9.166622e+22
[22,] 9.176200e+22 1.193368e+23 1.444775e+23 1.263429e+23 1.377717e+23
[23,] 2.112916e+22 2.747868e+22 3.326782e+22 2.909195e+22 3.172196e+22
[24,] 1.025411e+23 1.333547e+23 1.614477e+23 1.411836e+23 1.539603e+23
[25,] 6.655130e+22 8.655013e+22 1.047834e+23 9.163130e+22 9.992153e+22
[26,] 5.964395e+22 7.756732e+22 9.390861e+22 8.212122e+22 8.954811e+22
[27,] 7.364280e+22 9.577294e+22 1.159497e+23 1.013957e+23 1.105654e+23
[28,] 8.116931e+22 1.055614e+23 1.278006e+23 1.117588e+23 1.218637e+23
[29,] 8.686331e+22 1.129663e+23 1.367651e+23 1.195984e+23 1.304149e+23
[30,] 7.777872e+22 1.011512e+23 1.224601e+23 1.070895e+23 1.167805e+23
                                                                      
 [1,] 9.046767e+22 1.359648e+23 3.130733e+22 1.519363e+23 9.860985e+22
 [2,] 6.815789e+22 1.024406e+23 2.358664e+22 1.144789e+23 7.429730e+22
 [3,] 5.496796e+22 8.260969e+22 1.902232e+22 9.231171e+22 5.991299e+22
 [4,] 2.257323e+22 3.392362e+22 7.811764e+21 3.790684e+22 2.460300e+22
 [5,] 7.454509e+22 1.120382e+23 2.579705e+22 1.252023e+23 8.125761e+22
 [6,] 5.932120e+22 8.915341e+22 2.052878e+22 9.962515e+22 6.465915e+22
 [7,] 6.876488e+22 1.033467e+23 2.379686e+22 1.154859e+23 7.495302e+22
 [8,] 7.960752e+22 1.196466e+23 2.754896e+22 1.337045e+23 8.677571e+22
 [9,] 9.641077e+22 1.448976e+23 3.336398e+22 1.619192e+23 1.050886e+23
[10,] 1.326879e+23 1.994221e+23 4.591798e+22 2.228515e+23 1.446338e+23
[11,] 7.083898e+22 1.064650e+23 2.451460e+22 1.189715e+23 7.721487e+22
[12,] 1.304797e+23 1.960952e+23 4.515405e+22 2.191265e+23 1.422191e+23
[13,] 6.666842e+22 1.001943e+23 2.307140e+22 1.119618e+23 7.266639e+22
[14,] 5.689673e+22 8.551336e+22 1.968967e+22 9.556080e+22 6.202001e+22
[15,] 6.890945e+22 1.035625e+23 2.384693e+22 1.157257e+23 7.510918e+22
[16,] 6.105617e+22 9.176200e+22 2.112916e+22 1.025411e+23 6.655130e+22
[17,] 7.940413e+22 1.193368e+23 2.747868e+22 1.333547e+23 8.655013e+22
[18,] 9.613271e+22 1.444775e+23 3.326782e+22 1.614477e+23 1.047834e+23
[19,] 8.406591e+22 1.263429e+23 2.909195e+22 1.411836e+23 9.163130e+22
[20,] 9.166622e+22 1.377717e+23 3.172196e+22 1.539603e+23 9.992153e+22
[21,] 6.522869e+22 9.802781e+22 2.257323e+22 1.095385e+23 7.109450e+22
[22,] 9.802781e+22 1.473264e+23 3.392362e+22 1.646319e+23 1.068498e+23
[23,] 2.257323e+22 3.392362e+22 7.811764e+21 3.790684e+22 2.460300e+22
[24,] 1.095385e+23 1.646319e+23 3.790684e+22 1.839758e+23 1.194022e+23
[25,] 7.109450e+22 1.068498e+23 2.460300e+22 1.194022e+23 7.749412e+22
[26,] 6.371800e+22 9.576017e+22 2.205037e+22 1.070069e+23 6.945050e+22
[27,] 7.867326e+22 1.182358e+23 2.722583e+22 1.321219e+23 8.575097e+22
[28,] 8.671566e+22 1.303201e+23 3.000906e+22 1.456234e+23 9.451462e+22
[29,] 9.279638e+22 1.394617e+23 3.211328e+22 1.558413e+23 1.011453e+23
[30,] 8.308651e+22 1.248754e+23 2.875290e+22 1.395476e+23 9.056797e+22
                                                                      
 [1,] 8.837514e+22 1.091174e+23 1.202696e+23 1.287064e+23 1.152456e+23
 [2,] 6.658347e+22 8.221083e+22 9.061119e+22 9.697001e+22 8.683338e+22
 [3,] 5.369569e+22 6.629853e+22 7.307522e+22 7.820038e+22 7.001968e+22
 [4,] 2.205037e+22 2.722583e+22 3.000906e+22 3.211328e+22 2.875290e+22
 [5,] 7.282224e+22 8.991396e+22 9.910223e+22 1.060558e+23 9.496729e+22
 [6,] 5.794870e+22 7.154971e+22 7.886266e+22 8.439436e+22 7.556697e+22
 [7,] 6.717403e+22 8.294029e+22 9.141733e+22 9.782984e+22 8.759750e+22
 [8,] 7.776758e+22 9.602003e+22 1.058323e+23 1.132581e+23 1.014163e+23
 [9,] 9.418111e+22 1.162860e+23 1.281705e+23 1.371620e+23 1.228177e+23
[10,] 1.296204e+23 1.600430e+23 1.763985e+23 1.887746e+23 1.690354e+23
[11,] 6.920060e+22 8.544245e+22 9.417482e+22 1.007813e+23 9.024135e+22
[12,] 1.274601e+23 1.573761e+23 1.734618e+23 1.856282e+23 1.662104e+23
[13,] 6.512546e+22 8.041097e+22 8.863004e+22 9.484630e+22 8.492455e+22
[14,] 5.558173e+22 6.862703e+22 7.564002e+22 8.094735e+22 7.248392e+22
[15,] 6.731469e+22 8.311402e+22 9.160932e+22 9.803461e+22 8.777947e+22
[16,] 5.964395e+22 7.364280e+22 8.116931e+22 8.686331e+22 7.777872e+22
[17,] 7.756732e+22 9.577294e+22 1.055614e+23 1.129663e+23 1.011512e+23
[18,] 9.390861e+22 1.159497e+23 1.278006e+23 1.367651e+23 1.224601e+23
[19,] 8.212122e+22 1.013957e+23 1.117588e+23 1.195984e+23 1.070895e+23
[20,] 8.954811e+22 1.105654e+23 1.218637e+23 1.304149e+23 1.167805e+23
[21,] 6.371800e+22 7.867326e+22 8.671566e+22 9.279638e+22 8.308651e+22
[22,] 9.576017e+22 1.182358e+23 1.303201e+23 1.394617e+23 1.248754e+23
[23,] 2.205037e+22 2.722583e+22 3.000906e+22 3.211328e+22 2.875290e+22
[24,] 1.070069e+23 1.321219e+23 1.456234e+23 1.558413e+23 1.395476e+23
[25,] 6.945050e+22 8.575097e+22 9.451462e+22 1.011453e+23 9.056797e+22
[26,] 6.224332e+22 7.685235e+22 8.470769e+22 9.064884e+22 8.116618e+22
[27,] 7.685235e+22 9.489027e+22 1.045894e+23 1.119249e+23 1.002163e+23
[28,] 8.470769e+22 1.045894e+23 1.152808e+23 1.233650e+23 1.104574e+23
[29,] 9.064884e+22 1.119249e+23 1.233650e+23 1.320176e+23 1.182077e+23
[30,] 8.116618e+22 1.002163e+23 1.104574e+23 1.182077e+23 1.058484e+23

E) Radius, Diameter and Girth

Eccentricity

 [1] 3 3 3 4 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 4 3 3 3 4 3 3 3

Radius

[1] 3

Diameter

[1] 4

Girth

$girth
[1] 3

$circle
+ 3/30 vertices, from c1f6e70:
[1]  5  1 27

F) Density

Density

[1] 0.2091954

G) Induced Graph

H)degree, pathesLength, edge avarage

degree’s average

[1] 6.066667

avarage of pathes length

[1] 2.036782

edge’s avarage

[1] 3.033333

I)clustering coefficient

local clustering coefficient

 [1] 0.33333333 0.04761905 0.30000000 0.00000000 0.06666667 0.10000000
 [7] 0.20000000 0.10714286 0.28571429 0.20000000 0.20000000 0.19444444
[13] 0.20000000 0.10000000 0.30000000 0.20000000 0.14285714 0.40000000
[19] 0.33333333 0.07142857 0.00000000 0.33333333 0.00000000 0.21428571
[25] 0.20000000 0.30000000 0.20000000 0.04761905 0.19047619 0.09523810

global clustering coefficient

[1] 0.1845238

A)erdosRenyi Graph With Direction

B)Transposed

C)Subdivision Graph

---

+ 204/204 edges from c4661dd:
  [1]  1->31 31->30  3->32 32-> 1 18->33 33-> 1 19->34 34-> 1 27->35 35-> 1
 [11] 13->36 36-> 2 19->37 37-> 2 13->38 38-> 3 23->39 39-> 3 30->40 40-> 3
 [21]  2->41 41-> 4  5->42 42-> 4  9->43 43-> 4 11->44 44-> 4 14->45 45-> 4
 [31] 24->46 46-> 4 15->47 47-> 5 28->48 48-> 5  5->49 49-> 6 10->50 50-> 6
 [41] 15->51 51-> 6 28->52 52-> 6  4->53 53-> 7 11->54 54-> 7 14->55 55-> 7
 [51] 23->56 56-> 7  4->57 57-> 8 25->58 58-> 8 18->59 59-> 9 21->60 60-> 9
 [61] 25->61 61-> 9  6->62 62->10 23->63 63->10 24->64 64->10  7->65 65->11
 [71] 21->66 66->11 28->67 67->11  5->68 68->12 10->69 69->12 23->70 70->12
 [81] 28->71 71->12  1->72 72->13  5->73 73->13 30->74 74->13  5->75 75->14
 [91] 16->76 76->14 20->77 77->14 27->78 78->14  5->79 79->15  6->80 80->15
+ ... omitted several edges

D)Hamiltonian Cycle

E)Adjecency Matrix

30 x 30 sparse Matrix of class "dgCMatrix"
                                                                 
 [1,] . . . . . . . . . . . . 1 . . . . . . . . . . 1 . 1 . . . 1
 [2,] . . . 1 . . . . . . . . . . . . . . . . . 1 . . 1 . . . . .
 [3,] 1 . . . . . . . . . . . . . . . . . . . . . 1 . . . . 1 . .
 [4,] . . . . . . 1 1 . . . . . . . . . . . . . . . . . . . . . .
 [5,] . . . 1 . 1 . . . . . 1 1 1 1 . 1 . . . 1 . . 1 . . . . . .
 [6,] . . . . . . . . . 1 . . . . 1 . . . 1 . . . . . . . . . 1 .
 [7,] . . . . . . . . . . 1 . . . . . . . . . . . 1 . . . . . . .
 [8,] . . . . . . . . . . . . . . . . 1 . . . . 1 . . . . . . 1 .
 [9,] . . . 1 . . . . . . . . . . . . 1 . . . . . . . . . 1 . 1 .
[10,] . . . . . 1 . . . . . 1 . . . 1 . . . . . . . . . . . . . .
[11,] . . . 1 . . 1 . . . . . . . . . 1 . . . . . . . . . . . . .
[12,] . . . . . . . . . . . . . . 1 . . . . . . . . . . . . 1 1 .
[13,] . 1 1 . . . . . . . . . . . . . . . . . . . . . . 1 . . . .
[14,] . . . 1 . . 1 . . . . . . . . 1 . . 1 . . . . . . . 1 . . .
[15,] . . . . 1 1 . . . . . . . . . . . . . . . . . 1 . . . . . .
[16,] . . . . . . . . . . . . . 1 . . 1 . . 1 . . . . . 1 . . . .
[17,] . . . . . . . . . . . . . . . . . . 1 . . . 1 . . . . . . .
[18,] 1 . . . . . . . 1 . . . . . 1 . . . . . . . . . . . . . . .
[19,] 1 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
[20,] . . . . . . . . . . . . . 1 . . . . . . . 1 . . . . . . . .
[21,] . . . . . . . . 1 . 1 . . . . . . . 1 . . . . . 1 . . . . .
[22,] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
[23,] . . 1 . . . 1 . . 1 . 1 . . 1 . . . . . . 1 . . . . . . . .
[24,] . . . 1 . . . . . 1 . . . . . . . . . . . 1 . . . . . . . .
[25,] . . . . . . . 1 1 . . . . . . . . . . . . 1 . 1 . . . . . 1
[26,] . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
[27,] 1 . . . . . . . . . . . . 1 . . 1 1 . . 1 . . . 1 . . . . .
[28,] . . . . 1 1 . . . . 1 1 . . . . . . . . . . . . . . . . . .
[29,] . . . . . . . . . . . . . . . . . 1 . . . . . . . . . . . 1
[30,] . . 1 . . . . . . . . . 1 . . . . . . 1 . . . . . . . 1 . .

F)Radius, Diameter and Girth

Eccentricity

 [1] 3 3 3 3 2 3 3 3 3 3 3 3 3 3 3 3 2 3 3 3 3 3 3 3 3 3 3 3 3 3

Radius

[1] 2

Diameter

[1] 6

Girth

$girth
[1] 3

$circle
+ 3/30 vertices, from c35d93b:
[1]  3  1 13

G)Induced Graph

H)degree, pathesLength, edge avarage

degree’s average

[1] 3.4

avarage of pathes length

[1] 4.524138

edge’s avarage

[1] 3.4

I)clustering coefficient

local clustering coefficient

 [1] 0.21428571 0.10000000 0.26666667 0.14285714 0.12727273 0.07142857
 [7] 0.13333333 0.10000000 0.28571429 0.06666667 0.06666667 0.19047619
[13] 0.26666667 0.08333333 0.14285714 0.06666667 0.03571429 0.30000000
[19] 0.04761905 0.16666667 0.20000000 0.20000000 0.05555556 0.14285714
[25] 0.21428571 0.33333333 0.21428571 0.14285714 0.06666667 0.17857143

global clustering coefficient

[1] 0.1744186

A)erdosRenyi Graph With Direction and wieght

       [,1] [,2] [,3]
  [1,]    9    1   81
  [2,]   19    1   71
  [3,]    5    2   89
  [4,]   28    2   63
  [5,]    2    3   35
  [6,]    5    3   11
  [7,]    7    3   94
  [8,]   11    3   98
  [9,]   16    3   17
 [10,]   19    3    4
 [11,]   20    3   77
 [12,]    2    4   74
 [13,]    3    4   44
 [14,]    8    4   89
 [15,]   11    4   14
 [16,]    9    5   59
 [17,]   23    5   46
 [18,]    3    6   28
 [19,]    8    6    3
 [20,]   26    6   83
 [21,]   28    6   91
 [22,]    1    7   76
 [23,]    3    7   12
 [24,]    7   30   23
 [25,]    9    7   73
 [26,]   12    7    2
 [27,]   16    7   84
 [28,]   19    7    6
 [29,]   29    7   72
 [30,]    4    8   11
 [31,]    7    8   20
 [32,]   18    8   83
 [33,]    1    9   68
 [34,]   13    9   85
 [35,]   16    9   85
 [36,]   19    9    5
 [37,]   23    9   63
 [38,]    1   10    5
 [39,]    2   10   53
 [40,]    6   10   54
 [41,]   12   10   91
 [42,]    7   11   15
 [43,]    8   11   75
 [44,]   29   11   66
 [45,]    2   12    6
 [46,]    7   12   70
 [47,]   14   12   67
 [48,]   30   12   61
 [49,]    6   13   34
 [50,]   12   13   67
 [51,]    5   14   72
 [52,]   11   14   59
 [53,]   18   14   21
 [54,]   27   14   68
 [55,]   29   14   66
 [56,]    6   15   90
 [57,]    8   15   49
 [58,]   16   15   85
 [59,]   19   15   40
 [60,]   20   15   55
 [61,]   22   15   44
 [62,]    4   16   42
 [63,]   28   16   86
 [64,]    5   18   23
 [65,]    9   18   30
 [66,]   17   18   84
 [67,]   25   18   35
 [68,]    2   19   17
 [69,]    6   19   35
 [70,]   10   19   77
 [71,]   13   19   56
 [72,]   18   19   22
 [73,]   27   19   74
 [74,]   12   20   72
 [75,]   26   20   76
 [76,]   18   21   43
 [77,]   26   21   53
 [78,]    1   22   17
 [79,]   11   22   45
 [80,]   24   22   58
 [81,]    2   23   32
 [82,]    6   23   75
 [83,]   13   23   58
 [84,]   16   23    4
 [85,]   17   23   21
 [86,]   11   24   15
 [87,]   13   24   82
 [88,]   24   30   89
 [89,]   15   25   36
 [90,]   22   25   90
 [91,]   26   30    3
 [92,]    4   27   65
 [93,]   10   27   82
 [94,]   11   27   91
 [95,]   28   27   22
 [96,]   29   27    4
 [97,]   30   27   89
 [98,]   14   28    4
 [99,]   22   28   52
[100,]   26   28   85
[101,]    1   29    0
[102,]   17   29   80
[103,]   18   29   73
[104,]   22   29   66

B)subGraph

      [,1] [,2] [,3]
 [1,]    5    3   11
 [2,]   16    3   17
 [3,]   19    3    4
 [4,]   11    4   14
 [5,]    3    6   28
 [6,]    8    6    3
 [7,]    3    7   12
 [8,]    7   30   23
 [9,]   12    7    2
[10,]   19    7    6
[11,]    4    8   11
[12,]    7    8   20
[13,]   19    9    5
[14,]    1   10    5
[15,]    7   11   15
[16,]    2   12    6
[17,]   18   14   21
[18,]    5   18   23
[19,]    2   19   17
[20,]   18   19   22
[21,]    1   22   17
[22,]   16   23    4
[23,]   17   23   21
[24,]   11   24   15
[25,]   26   30    3
[26,]   28   27   22
[27,]   29   27    4
[28,]   14   28    4
[29,]    1   29    0

C)MST

      [,1] [,2] [,3]
 [1,]    5    3   11
 [2,]   16    3   17
 [3,]   19    3    4
 [4,]   11    4   14
 [5,]    8    6    3
 [6,]    7   30   23
 [7,]   12    7    2
 [8,]   19    7    6
 [9,]    4    8   11
[10,]   19    9    5
[11,]    1   10    5
[12,]    7   11   15
[13,]    2   12    6
[14,]    6   13   34
[15,]   18   14   21
[16,]   20   15   55
[17,]   25   18   35
[18,]   18   19   22
[19,]   18   21   43
[20,]    1   22   17
[21,]   16   23    4
[22,]   17   23   21
[23,]   11   24   15
[24,]   15   25   36
[25,]   26   30    3
[26,]   28   27   22
[27,]   29   27    4
[28,]   14   28    4
[29,]    1   29    0

D) Radius, Diameter, Girth

Eccentricity

 [1] 3 3 3 3 3 3 3 2 3 3 3 3 3 3 3 3 4 3 2 4 3 3 3 3 3 3 3 3 3 3

Radius

[1] 2

Diameter

[1] 261

Girth

$girth
[1] 3

$circle
+ 3/30 vertices, from c4724bc:
[1] 7 1 9

E)degree, pathesLength, edge avarage

degree’s average

[1] 180.5

avarage of pathes length

[1] 5.289655

edge’s avarage

[1] 3.466667

F)clustering coefficient

local clustering coefficient

 [1] 0.28571429 0.21428571 0.20000000 0.23809524 0.33333333 0.19444444
 [7] 0.16666667 0.14285714 0.27777778 0.33333333 0.30555556 0.07142857
[13] 0.26666667 0.28571429 0.14285714 0.19047619 0.33333333 0.13888889
[19] 0.25454545 0.00000000 0.00000000 0.19047619 0.23809524 0.16666667
[25] 0.33333333 0.10000000 0.21428571 0.09523810 0.32142857 0.10000000

global clustering coefficient

[1] 0.2325949

A) Multi Graph

B)degree, pathesLength, edge avarage

degree’s average

[1] 3.733333

avarage of pathes length

[1] 1.628571

edge’s avarage

[1] 1.866667

C)clustering coefficient

local clustering coefficient

 [1] 0.05747126 0.18382353 0.50000000 0.50000000 0.50000000 0.50000000
 [7] 0.50000000 0.50000000 0.50000000 0.50000000 0.50000000 0.50000000
[13] 0.50000000 0.50000000 0.18382353

global clustering coefficient

[1] 0.3592233

A) Watts Strogatz Graph With 30 Node

B)degree, pathesLength, edge avarage

degree’s average avarage of pathes length edge’s avarage

C)clustering coefficient

local clustering coefficient global clustering coefficient

D) Watts Strogatz Graph With 300 Node